The integrating factor of differential e

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Differential Equations

Question:

The integrating factor of differential equation $x\frac{dy}{dx}$+2y=x² log x is

Options:

$\frac{1}{x}$

$\frac{1}{x^2}$

x²

Correct Answer:

x²

Explanation:

$x.\frac{dy}{dx}+2y=x^2logx$

$\frac{dy}{dx}+\frac{2}{x}×y=xlogx⇒\frac{dy}{dx}+\frac{2y}{x}=xlogx$

$P=\frac{2}{x}$

$I.F.=e^{\int\frac{2}{x}dx}=e^{2logx}=x^2$

Option 4 is correct.